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Algebra and Geometry Formulas & Words
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Math formulas for Algebra and Geometry. THERE ARE IMPORTANT WORDS & DEFINITIONS TO REMEMBER AS WELL!
Terms in this set (121)
PEMDAS
Please Excuse My Dear Aunt Sally
1.Parentheses
2.Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction
7. Solve the problem from left to right
How to find Slope?
Slope=Rise/Run
Guess my rule formula
Next=Now+/- a number
Formula for linear equation for the missing number in the table
1. M= y 2 - y 1/x 2 - X 1
Y=m x+b
Formula for inequalities
x is greater than/less than or equal to number. if the line is under the less or greater sign, then it is closed circle. And if the line is not under the less or greater sign, then it is open sign.
line
goes without end in both directions.
ray
has 1 endpoint and goes without end in 1 direction.
line segment
has 2 endpoints. A part of line with a definite length. The endpoints may be labeled.
Intersecting line
meet at one point.
Parallel line
stay the same distance apart. They will never intersect.
Perpendicular line
meet at right angles. They make square corners.
Sort Objects and Data
Sort the objects out by their attributes/common factors.
Example: Odd and Evens
More/less than
Odd < 10: 5, 7, 9 Even<10: 2,4
Odd>10: 31,45 Even>10: 12, 20, 32, 36, 50
Data:
Younger than my age: 2, 4, 5, 7, 9, 12
My age:
Older than my age: 20, 31, 32, 36, 45, 50
Object
A thing that you can touch or feel.
Groups
Collection of objects or numbers.
Assemble
To place objects or numbers in a groups.
Attribute
Something about the object or number that allows to fit into a group.
Data
A collection of numbers.
Record
to write down.
Frequency
how often something occurs.
Order
To assemble in a defined way
Collect
To assemble into a group.
Determining Frequency
EXAMPLE: List each different number/count the number the times each number occurs. DO NOT DIVIDE !
Represent
Use a method to show data.
Display
To list, show.
Methods
Lists, graphs, tally charts, tables, bar graphs, pictographs and so on.
Frequency
A count of an object or number.
Data Set
A group of data.
Fraction
Part of a whole (Examples: 1/4, 1/2 or 0.25, 0.5)
Percent
Part of 100. Examples: 57/100= 57%.
Event
Something that happens or something that may happen.
Probability
How likely it is that an event will happen.
Outcome
The result of an event such as tossing a coin.
Theoretical probablity
The probability of an event based on the number of possible and the total number of outcomes.
Metric Ruler
A ruler showing millimeters, centimeters, or meters.
Customary ruler
A ruler showing inches, feet, or yards.
Polygon
A closed figure formed from line segments that meet only at their endpoints.
Perimeter
The sum of the lengths of the sides of a figure.
How to figure out perimter
1. Find the lengths of all sides.
2. Add all of the sides.
plane
A flat surface that goes on forever in all directions
Formula for a rectangle (Perimeter/Area)
Perimeter = l + l + w + w = 2 × l + 2 × w
Area = l × w
Formula for a square (Perimeter/Area)
Perimeter = s + s + s + s = 4 × s
Area = s2
Formula for a Parallelogram (Perimeter/Area)
Perimeter = a + a + b + b = 2 × a + 2 × b
Area = b × h
Formula for a Rhombus (Perimeter/Area)
Perimeter = b + b + b + b = 4 × b
Area = b × h
Formula for a Triangle (Perimeter/Area)
Perimeter = a + b + c
Area = (b × h)/2
1/2xbh
Formula for a Trapezoid (Perimeter/Area)
Perimeter = a + b + c + d
Formula for a circle (Perimeter/Area)
Perimeter = 2 × pi × r or Perimeter = pi × d
Area = pi × r2 or Area = (pi × d2)/4
square
a2
rectangle
ab
parallelogram
bh
trapezoid
h/2 (b1 + b2)
circle
pi r 2
ellipse
pi r1 r2
triangle
(1/2) b h
equilateral triangle
(1/4)(3) a2
triangle given SAS
(1/2) a b sin C
triangle given a,b,c
[s(s-a)(s-b)(s-c)] when s = (a+b+c)/2 (Heron's formula)
regular polygon
(1/2) n sin(360°/n) S2
Volumes
.....
cube
a3
rectangular prism
A=lw
Example:Front 6x2=12ft2
Bottom:6x8=48ft2
End:8x2=16ft2
Surface Area=2(12)+2(48)+2(16)=24+96+32=152 square feet
irregular prism
b h
cylinder
b h = r2 h
pyramid
(1/3) b h
cone
(1/3) b h = 1/3 r2 h
sphere
(4/3) r3
ellipsoid
(4/3) pi r1 r2 r3
Surface Areas
The total area of all of the faces.
cube
6 a2
prism
(lateral area) = perimeter(b) L
(total area) = perimeter(b) L + 2b
sphere
4 r2
Area of a circumfernece
c=pid
Calculate circumference using the radius:
C= 2 pi r
Area of a circle
A= pir2
volume of a triangular prism
B=1/2bh
volume of a cylinder
V=bh
B=pir2
How to find a perimeter on a Coordinate Grid
Step 1: Find the length of the vertical segments. Since one pair of vertical segments has (-3,2) and (-3,-1) the length is the difference of the y-coordinates 2-(-1), or 3.
Step 2: Find the length of the horizontal segments. Since one pair of horizontal segments has coordinates (-3,2) and (4,2) the length is the difference of the x-coordinates 4-(-3) or 7. The perimeter of the rectangle is 3+3+7+7.
Perimeter of a triangle
Add all of the sides of the Triangle and it will equal this many inches.
Perimeter of a rectangle
Add all of the sides of rectangle and it will give your solution.
Rectangle
A 4-sided figure with opposite sides parallel and with four right angles.
Area
The measure, in square units, of the interior region of a 2-dimensional figure or of the surface of a 3-dimensional figure.
Square Inch
The area of a square one inch long and one inch wide.
Measuring the Area of a Rectangle
Step 1: Measure the sides of the rectangle
Find the length= 4 inches
Find the width= 1.25 inches
Step 2: 4 inches X 1.25 inches= 5 square inches.
Quadrilateral
A four sided polygon.
Parallelogram
A quadrilateral with both pairs of opposite sides. parallel and equal.
Height
A measure of the perpendicular distance between two lines.
Area of a parrelogram
Base into height= square centimeters, etc.
Triangle
A polygon with three sides.
How to circumfernce
C=d
pi= 3.14
D= Diameter.
Center
A point that is the same distance from all points on a circle.
Circle
A closed curve in a plane who's points are the same distance from a fixed point called the center.
Circumfernce
The perimeter of a circle, or distance around a circle.
Diameter
The length of a segment through the center of the circle connecting two points of the circle.
Formula for Radius
C=2 x pi into radius.
Prism
A three-dimensional figure with two parallel bases that are the same polygons
Lateral Face
A face of a prism that is not base.
Rectangular prism
a prism with six rectangular faces.
Volume
The amount of space inside a 3-D figure.
Base of prsim
The top or bottom face.
Volume of a prism
Area of base Formula: B=l x w; B= 7 x 2 = 14 cm 2
Volume formula= V= Bh
Triangular Prism
A prism with two bases that are triangles.
Volume of a right triangular prism
B=1/2bh
=c
Cylinder
A 3-D figure with two parallel bases that are circles.
Volume of a cylinder
V= Bh
B= pi into r 2
Angle
a figure formed by two rays that have the same end point.
Vertax
The point where two rays meet.
Acute angle
angle with measure less than 90 degrees.
Right angle
angle with measure 90 degrees.
Obtuse angle
angle with measure greater than 90 degrees and less than 180.
Straight angle
angle with measure 180.
Complementary angles
two angles whose sum is 90. example: 30 and 60 is 90.
Supplementary angles
two angles whose sum is 180. 30 and 150.
Find the complement of an angle
m<A = 64
m<B= 27
Finding the Supplement of an angle
m<C= 104
m<D= 121
Measure of the angle
add the two given angles.
subtract the sum from 180
This also applies to the quadrilateral. Missing angles from a quadrilateral (360) triangle
Hypotenuse
the side of a right triangle opposite the right angle.
Legs
the sides of a right triangle that form the right triangle.
Pythagorean Theorem
a 2 + b 2= c 2
Finding the Hypotenuse
add and take the square root.
Converse
the converse of an if-then sentence is obtained by reversing the two parts of the sentence.
Congruent figures
figures that have the same size and shape.
Corresponding parts
the sides or angle that are in corresponding positions in congruent figures.
Similar figures
figures that have the same shape but not the same size.
Use the proportion to solve a problem .
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